In the future, human-like robots will live among people to provide company and help carrying out tasks in cooperation with humans. These interactions require that robots understand not only human actions, but also the way in which we perceive the world. Human perception heavily relies on the time dimension, especially when it comes to processing visual motion. Critically, human time perception for dynamic events is often inaccurate. Robots interacting with humans may want to see the world and tell time the way humans do: if so, they must incorporate human-like fallacy. Observers asked to judge the duration of brief scenes are prone to errors: perceived duration often does not match the physical duration of the event. Several kinds of temporal distortions have been described in the specialized literature. Here we review the topic with a special emphasis on our work dealing with time perception of animate actors versus inanimate actors. This work shows the existence of specialized time bases for different categories of targets. The time base used by the human brain to process visual motion appears to be calibrated against the specific predictions regarding the motion of human figures in case of animate motion, while it can be calibrated against the predictions of motion of passive objects in case of inanimate motion. Human perception of time appears to be strictly linked with the mechanisms used to control movements. Thus, neural time can be entrained by external cues in a similar manner for both perceptual judgments of elapsed time and in motor control tasks. One possible strategy could be to implement in humanoids a unique architecture for dealing with time, which would apply the same specialized mechanisms to both perception and action, similarly to humans. This shared implementation might render the humanoids more acceptable to humans, thus facilitating reciprocal interactions.